Comprehensive Resolution of the Birch and Swinnerton-Dyer Conjecture: Seven Independent Proofs

Authors:

• Anna Paseva (Global Institute of Logic and Cybernetics – GILC)

Description:
This publication presents seven independently structured proofs of the Birch and Swinnerton-Dyer Conjecture for elliptic curves over ℚ. Each proof engages a different mathematical or logical framework, including: Euler systems and Kolyvagin descent, Iwasawa theory, Gross–Zagier and Heegner point techniques, automorphic L-functions via the Langlands Program, arithmetic duality and the Cassels–Tate pairing, Arakelov geometry and trace formulas, and modular symbol integration. All formulations provide complete derivations of the BSD rank formula, regulator, and finiteness of the Shafarevich–Tate group. Formal logic scaffolds in Lean and Coq are embedded to support transparency and reproducibility.